Column

Assumptions

Base Currency

DKK

Signif Value

97.5%

Column

Input data for the the backtest

The figure shows daily Value-at-risk & Expected Shortfall risk predictions together with daily Profit/Loss observations. The “red” dots highlights the Value-at-Risk-events where the Profit/Loss is worse (more negetive) than predicted by Value-at-Risk.

Column

Summary of the backtest

Backtest Results
Value-at-Risk & Expected Shortfall
Year #VaR-Events #Obs ES-Test-Stat Test for Accuracy (p-value)
Value-at-Risk1 Expected-Shortfall1
By year
2018 5 260 0.1341 p-value >= 0.1 p-value >= 0.1
2019 5 261 0.2167 p-value >= 0.1 p-value >= 0.1
2020 7 262 -0.1552 p-value >= 0.1 p-value >= 0.1
2021 6 261 0.0846 p-value >= 0.1 p-value >= 0.1
2022 6 193 -0.1050 p-value >= 0.1 p-value >= 0.1
All years
29 1,237 0.0425 p-value >= 0.1 p-value >= 0.1
Reference: Carlo Acerbi & Balazs Szekely (2014) BACKTESTING EXPECTED SHORTFALL, MSCI. The unconditional test statistic (test 2) are used here

1 The p-value tells you how likely it is to observe a worse outcome under the null hypothesis of an accurate model.

The summary of the backtest is created based on the daily input-values for Profit/Loss, Value-at-Risk and Expected-Shortfall. The p-value can be interpretated as a likelihood of observing an even worse outcome than observed (i.e. more frequent loss-events for Value-at-Risk and more severe losses for Expected-Shortfall) under the assumption that the model is accurate (the null hypothesis). In case where the p-value is low this is used as evidence against the hypothesis and hence conclude that the model show signs of not being accurate.

Column

P-value Interpretation

Colour Schema
p-value
Interpretation
p-value >= 0.1
p-value < 0.1
p-value < 0.05
p-value < 0.02
p-value < 0.01
p-value < 0.005
p-value < 0.001
Reference: Basel Committee on Banking Supervision (2019) Minimum capital requirements for market risk, 'MAR99 Guidance on use of the internal models approach', table 2 (p. 128). The colour schema is an ENVISIONRISK adoptation of the chosen cutoff values in the BIS paper.

The interpretation of ‘p-value < 10%’ is that the p-value is higher than 5% but lower than 10%. The same rationale for the rest of the p-values. We dont calculate an exact p-value, but only calculte it for certain cutoff values.